Seeds need to be stored in a dark and dry place (ideally 5°C). Jerry Coleby-Williams uses old film canisters to store his seeds. Specimen bottles would work well, but I’m not sure where to buy them. To help keep the moisture out, add some silica gel crystals. (You may know these as the small white “Do Not Eat” bags you find in vitamin bottles).
I have found the best way to store my seeds is alphabetically in an IKEA cd box. If you want to get fancy try the Plant Agenda. Josh Byrne keeps his seed packets in use pinned to a cork board in his potting shed.
If you are storing your seeds for a long time the fridge might be the best place for them. Don’t forget seeds are living and they need to be sown and collected every couple of years.